Deuterium Fractionation in Warm Dense Interstellar Clumps

A&A 464, 245–252 (2007) Astronomy DOI: 10.1051/0004-6361:20066531 & c ESO 2007 Astrophysics

Deuterium fractionation in warm dense interstellar clumps

E. Roueﬀ1, B. Parise2,andE.Herbst3

1 LUTH, Observatoire de Paris, Section de Meudon, Place Jules Janssen, 92195 Meudon, France e-mail: [email protected] 2 Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany 3 Departments of Physics, Astronomy, and Chemistry, The Ohio State University, Columbus, OH 43210, USA Received 10 October 2006 / Accepted 12 December 2006

ABSTRACT

Aims. In a recently published 1-millimeter line survey of the Orion Bar by Leurini et al., the conﬁrmation of dense neutral clumps was reported based mainly on an analysis of methanol spectral lines. Within these clumps, a high abundance ratio was found between the deuterated isotopologue DCN and HCN. Methods. In this paper, we use steady-state chemical modelling to determine if the DCN/HCN abundance ratio can be understood in terms of gas-phase processes. Results. Our results show that, at temperatures (50−75 K) and densities (5−20 × 106 cm−3) in the vicinity of those measured, the calculated DCN/HCN abundance ratio can reach 0.01 or even higher, in good agreement with the measured range of 0.007−0.009. Moreover, the fractional abundance of HCN is also calculated to be in the vicinity of that reported. Other computed abundance ratios between deuterated and normal isotopologues are reported for the physical conditions of the clumps. The abundance ratios are analyzed as functions of temperature and density in terms of a simple formula. In general, calculated ratios can be somewhat dependent on the choice of two very diﬀerent sets of elemental abundances, one of which is the “standard” low-metal set, while the other we term the “warm-core” set. Key words. ISM: abundances – ISM: molecules – molecular processes

1. Introduction onto the grains and neutralization of electrons on grains allow +/ + the H2D H3 ratio to approach the high thermodynamic value, Deuterium fractionation is a well-known process in the dense in- although there are complications caused by ortho-para effects terstellar medium in which deuterated isotopologues of interstel- (Gerlich et al. 2002). Moreover, deuteration need not stop at lar molecules achieve abundances compared with normal species the singly-deuterated isotopologue; further exothermic reactions much higher than the deuterium-to-hydrogen elemental abun- + + with HD lead to both D2H and finally D3 (Roberts et al. 2003, dance ratio. Such fractionation can occur both in the gas phase 2004; Walmsley et al. 2004). At high enough depletions, calcu- and on the surfaces of dust particles. In the gas phase, the ori- lations lead to the bold prediction that the totally deuterated ion gin of the fractionation is mainly “thermodynamic” rather than is the most abundant of the four, although observations of the kinetic: ion-molecule reactions in which deuterium and hydro- rotational spectrum of this ion are not possible because it does gen atoms from reservoirs (H2 and HD) are exchanged proceed not possess a permanent dipole moment. The recent detection much more rapidly in the exothermic direction at low tempera- + of D2H does offer strong support for this picture of deuterium tures. As an example, consider the dominant system at a typical fractionation (Vastel et al. 2004). temperature for a cold source of 10 K: + The production of deuterated ions from H3 leads to high + + + + . abundances of other deuterated species through secondary ion- H3 HD H2D H2 (1) molecule reactions, as the deuterated ions react with a variety of neutral species. Not only singly deuterated isotopologues The reaction that proceeds in the left-to-right direction is are produced by secondary reactions involving deuterated ions; exothermic by 232 K (Gerlich et al. 2002) both because of dif- species such as NHD ,ND ,andD CO are observed and under- ferences in zero-point vibrational energies and the non-existence 2 3 2 + stood at least partially in terms of gas-phase syntheses (Roberts of the ground rotational state of H due to the Pauli Exclusion 3 & Millar 2000; Gerin et al. 2006; Osamura et al. 2005; Roueff Principle. Thus, at low temperatures, the endothermic reaction + et al. 2005). Although H is not the only important molecular ion occurs slowly, and the equilibrium constant becomes very large, 3 +/ + to exchange deuterons with HD exothermically and rapidly, it is raising the abundance ratio H2D H3 to values much higher than −5 the most abundant under most conditions. Two other ions that the HD/H2 reservoir value of 3 × 10 . Normally this “ther- + + + react rapidly with HD – CH3 (Asvany et al. 2004) and C2H2 +/ + H2D ≈ modynamic equilibrium ” value for the H2D H3 ratio ( H+ (Gerlich & Schlemmer 2002) – are also of some importance, 3 + + HD × / leading to the ions CH2D and C2HD (Herbst et al. 1987; H exp(232 T) ) is not reached because the destruction of the 2 + Millar et al. 1989): ion H2D is dominated by reactions with heavy species such + + as CO and by recombination with electrons. At high densities CH + HD CH2D + H2, (2) and low temperatures, however, such as pertain to the centers of 3 + + + + . so-called pre-stellar cores, accretion of heavy gas-phase species C2H2 HD C2HD H2 (3)

Article published by EDP Sciences and available at http://www.aanda.org or http://dx.doi.org/10.1051/0004-6361:20066531 246 E. Roueﬀ et al.: Deuterium fractionation in warm clumps

+ The left-to-right exothermicities, ≈390 K (Asvany et al. 2004) reactions involving CH2D ”. In this paper, we report a study of and ≈550 K (Herbst et al. 1987), respectively, are considerably the deuterium fractionation that can occur under the conditions + larger than for the reaction involving H3 . of the warm clumps in the Orion Bar at steady-state. Our results Detailed gas-phase models including deuterated species have show that the hypothesis of Leurini et al. (2006) is indeed cor- been constructed using large networks of gas-phase reactions rect, and also reveal some interesting features such as a strong with both the steady-state and pseudo-time-dependent pictures direct density dependence to the fractionation, which occurs in (Millar et al. 1989; Roberts & Millar 2000; Turner 2001; Millar the absence of depletion onto grains for two very different sets 2002; Gerlich et al. 2002; Roberts et al. 2004; Roueff et al. of elemental abundances chosen. 2005). A rather complete discussion of the complex chem- In the remainder of the paper, we first discuss the chemical istry of deuteration at temperatures up to 40 K and densities model used. In Sect. 3, our results for DCN/HCN and other ra- through 105 cm−3 has been given by Turner (2001). The cal- tios are discussed and interpreted in terms of limited reactions, culated ratios between deuterated and normal isotopologues are while in the last section, we discuss the results in terms of the often in quantitative agreement with observations, and it is typ- observations of Leurini et al. (2006). ically found that there is much less time-dependence to the calculated ratios than to calculated fractional abundances, so that 2. Chemical model and model parameters steady-state approximations are often useful. Some models include depletion of gas-phase species in an active sense (Roberts The Meudon gas-phase network (Gerlich et al. 2002; Roueff et al. 2002), while others even include surface fractionation pro- et al. 2005) has been used for this study. This network comprises cesses (Aikawa et al. 2005). Fractionation on grain surfaces is 218 species including multideuterated isotopologues involving thought to occur following the formation of a large atomic D/H the elements C, N, O and S connected by more than 3250 gas ratio in the gas. The deuterium and hydrogen atoms, after land- phase chemical reactions. It should be noted that all deuter- + + + ing on surfaces, then react with a variety of heavy species leading ated isotopologues of Hn ,HnCO ,andHnCS withnuptoa + to both deuterated and normal isotopologues (Tielens 1983). A value of 3, CHn with n up to a value of 5, molecular hydro- key series of processes leads to the deuterated isotopologues of gen, water, ammonia, formaldehyde, and thioformaldehyde are methanol, which are produced on grain surfaces by hydrogena- included in the network. However, the chemical network does tion and deuteration of CO (Charnley et al. 1997; Stantcheva & not include methanol chemistry, because it does not occur in the Herbst 2003; Nagaoka et al. 2005). gas phase. No distinction is made here between para and ortho + As temperature increases, the deuterium fractionation forms of the various isotopologues of the H3 molecular ions. achieved by gas-phase processes generally becomes less notice- Neutralization of atomic ions on grain surfaces is taken into ac- able for a variety of reasons. Most importantly, the abundance count as described in Le Bourlot et al. (1995). Neutralization of ratios between deuterated and normal ions achieved in exchange molecular ions on grain surfaces is less important because it is reactions are reduced as the endothermic reactions become more much slower than dissociative recombination with electrons in rapid. The extent of this reduction versus increasing tempera- the gas. If we consider classical grains with radius 0.1 µ,therate ture is a function of the exothermicity of the reaction system: coefficient for ballistic accretion is typically 3 × 10−6 cm3 s−1 + ffi since the exothermicity of exchange reactions of HD with CH3 whereas the rate coe cient for dissociative recombination is + + −6 3 −1 and C2H2 exceeds that of HD with H3 (Herbst et al. 1987), typically 10 cm s . Assuming a number density of grains deuterated isotopologues of the former can cause some general relative to H of 2.6 × 10−12 for classical grains and a fractional deuteration at higher temperatures, although the normal ions are ionization of at least 10−9, we see that dissociative recombina- + less abundant than H3 . Secondly, as the temperature increases, tion dominates unless one considers very small grains to be neg- depletions of heavy species onto grains are less and less likely. atively charged. Such small grains, when grouped with PAH’s, Indeed, desorption becomes important and can, for a limited are likely to have a fractional abundance of ≈10−7.Ifalargeper- time, enhance deuteration in the gas phase as the results of pre- centage are negatively charged, the recombination of atomic and vious fractionation on grain surfaces transfer to the gas. Such molecular ions may well be dominated by reactions with PAH− processes are thought to occur in hot cores and hot corinos, with rather than with electrons. On the other hand, the small amount kinetic temperatures of 100 K and larger, allowing the detec- of experimental evidence on the sticking of electrons to PAH tion of deuterated isotopologues of methanol in the gas phase neutrals shows that the rate coefficients are far smaller than esti- (Parise et al. 2002, 2004, 2006), although eventually the deuter- mated by astrochemists (Moustefaoui et al. 1998). The situation ation must reduce to the gas-phase value appropriate to the is currently being studied by Wakelam & Herbst. Pending a bet- temperature (Osamura et al. 2004). ter understanding of the abundance of PAH anions, we do not Recently, Leurini et al. (2006) used the APEX millimeter- include PAH’s in this analysis. and submillimeter-wave telescope to study the Orion Bar, per- The physical conditions of the warm clumps are assumed haps the best-known photon-dominated region (PDR), in the to be homogeneous. Since the history of the physical condi- 1 mm region. Looking at the Orion Bar (HCN) position, they tions of this matter is not known, it is simplest to assume that utilized methanol transitions to characterize a phase of warm the chemistry is at steady state. Although an early-time solu- 7 −3 (50−75 K), dense (nH = 1−4 × 10 cm )clumpsofmat- tion might lead to larger column densities of selected species, it ter originally studied by Lis & Schilke (2003). Moreover, they is our experience that calculated ratios of deuterated to normal detected DCN in this environment, and were able to estimate isotopologues are less sensitive to time dependence assuming aDCN/HCN abundance ratio (using the 13C isotopologue of constant physical conditions. We have performed calculations HCN) of 0.007−0.009. Leurini et al. (2006) speculated that, at temperatures from 10 K to 70 K and at gas densities n(H2) unlike the case of hot cores, the abundance ratio might actu- of 104−2 × 107 cm−3. Two sets of elemental abundances, shown ally reflect steady-state gas-phase conditions and, at the rather in Table 1, have been utilized for the gas-phase material. To ob- high temperature, the fractionation might be caused by reac- tain the first, known as “warm-core” abundances, we assume that + tions involving CH2D . As the authors state: “the Orion Bar some of the material comprising ice mantles in colder sources thus appears a unique reference to test the fractionation has desorbed into the gas. The second set of abundances closely E. Roueff et al.: Deuterium fractionation in warm clumps 247

Table 1. Elemental abundances with respect to the number of protons. Number in parenthesis refer to powers of ten.

Element Warm-core Low-metal He 0.10 0.10 O 3.0(–4) 1.8(–4) N 8.0(–5) 2.1(–5) C 2.0(–4) 7.3(–5) S 1.86(–5) 8.(–8) Fe 4.0(–7) 2.0(–8) resembles the well-known “low-metal” collection, which leads to best results for dark cold clouds such as L134N (Wakelam et al. 2006). The low-metal set features moderate depletions of C, N, and O and strong depletions of S and the only metal in the network, Fe. The elemental abundance of Fe is taken as the sum of all elemental abundances of metals in order to repro- duce the available electronic charges. The elemental abundance of helium, which is not condensable on the grain surfaces, is taken from Grevesse et al. (1996). Our value is 40% lower than the value used in the low-metal collection. In the warm-core set of elemental abundances, all depletions are reduced, with the in- Fig. 1. Deuterium fractionation ratios. Left: warm-core conditions, crease in sulphur being the most dramatic. The element Fe is de- ff right: low-metal conditions.The symbols for the assorted temperatures pleted by a factor of 20 less; this di erence will lead to a lower in this and subsequent figures are as follows: full squares (70 K), full fractional ionization in the low-metal case. The warm-core val- circles (60 K), open circles (50 K), open squares (40 K), full diamonds ues have some resemblance to the abundances used for PDR en- (30 K), full triangles (20 K), open diamonds (10 K). vironments, where the depletions are less strong. These choices are somewhat arbitrary but should mimic two possible extreme cases. that is most important at lower temperatures is the destruction by heavy species Ni and at higher temperatures the backward + exchange reaction. Note that the further reaction of H2D with + 3. Results HD to form D2H has been ignored because it is not important The results initially discussed here are in the form of figures of unless the Ni are depleted at low temperature. Both this reaction and the subsequent reaction of D H+ with HD to form D+ are in abundance ratios between deuterated and normal isotopologues 2 3 plotted against density for temperatures of 10, 20, 30, 40, 50, 60, our model. The case of CH D+/CH+ is a different story. The tempera- and70K. 2 3 ture dependence, which is the same for each set of elemental abundances, shows that the abundance ratio of the ions actually 3.1. Parent, or “primary,” deuterated ions increases in the range 10−40 K before decreasing at higher tem- + + peratures. To understand this dependence, one can again deter- We show in Fig. 1 the abundance ratios H2D /H and + + 3 mine the abundance ratio from an exchange reaction system and CH2D /CH with warm-core and low-metal abundances, re- + 3 +/ + other destruction reactions of CH2D . The equation: spectively. For the case of H2D H3 , there is very little density dependence with either set of elemental abundances, and CH D+ k HD 2 = f (5) the temperature dependence is the standard monotonic one once CH+ k + k + k e + k N the temperature gets higher than 20 K and the backwards rate 3 b ra dr i i i coefficient (see Eq. (1)) becomes important. When the temper- contains an extra term in the denominator when compared with + + ature reaches 60 K, the abundance ratio is just slightly larger the expression for H2D /H . This term derives from the radia- + 3 than 0.1%. The abundance ratio is easily obtained at steady state tive association of CH2D with H2, which has the estimated rate by consideration of the exchange reaction system plus the de- ffi = × −14 / −1.0 3 −1 + coe cient kra 2 10 (T 300) cm s (Roberts et al. struction of H2D by electrons and heavy species such as CO 2004). (Roberts et al. 2002). The simple equation obtained is: This destruction route is dominant for higher densities at + temperatures up to about 40 K, but decreases by a factor of 4 H2D kfHD from 10 K to 40 K. Around 40 K, the backwards rate coefficient, + = , (4) H kb + kdre + i kiNi kb, becomes equal with kra and at higher temperatures domi- 3 + nates. Interestingly, CH2D does not react rapidly with CO so where kf is the rate coefficient for the forward (exothermic) that its reaction with the heavy neutrals O and O2 are the domi- exchange reaction, kb is that for the backwards (endothermic) nant ones in this class, although they are not critical in this anal- process, kdr is the rate coefficient for the dissociative recom- ysis. Another factor in the temperature dependence is the rate co- + bination of H2D with electrons (e), and ki is the rate coefficient kf. The measured rate coefficient at 15 K (Asvany et al. efficient for reaction with heavy species, designated Ni.The 2004) is noticeably less than that at 80 K (Smith et al. 1982), abundances of all species are fractional with respect to H2.The and we have used an artificial activation energy of 15 K to pa- normal use of brackets for fractional abundances is omitted. rameterize the two measurements. This factor also helps enlarge Under the conditions studied here, the term in the denominator the direct temperature dependence seen in the 10−40 K range. 248 E. Roueff et al.: Deuterium fractionation in warm clumps

Unlike the temperature dependence, the density dependence dif- fers strongly between the two sets of abundances. The strong density dependence for the warm-core abundances is due to the greater fractional ionization at low densities, which strongly re- duces the ionic abundance ratio (see Eq. (5)) and lowers the +/ + temperature dependence. At 60 K, the CH2D CH3 abundance ratio still exceeds 0.01 for all densities with the low-metal abundances and for densities above 105 cm−3 with the warm-core abundances. + + The case of C2HD /C2H2 is rather similar to that of +/ + + + CH2D CH3 since C2HD , like C2H2 , should undergo a radiative association reaction with H2 (Gerlich & Schlemmer 2002). Theratecoeﬃcient of this reaction is estimated to be only + slightly larger than that for CH2D + H2. In discussing most of the secondary species below, we ignore processes starting + + from C2HD /C2H based on the ﬁnding that these ions are less 2 + + abundant than CH2D and CH3 under the conditions considered here and that they are less closely related to the particular secondary species studied. The exception concerns the radicals C2D and C2H.

3.2. Secondary species Fig. 2. Deuterium fractionation ratios. Left: warm-core conditions, In trying to understand the calculated abundance ratios between right: low-metal conditions. deuterated isotopologues and normal ones other than the parents, it is important to distinguish between deuteration during the formation of a species, and deuteration during the destruction of a of reacting ions. In general, f should not depend significantly + on n and T. Equation (7) contains the assumption that all ion- species. As an example of the former, consider the ion DCO . ffi This ion is formed at low temperatures primarily from the parent molecule rate coe cients are the same. H D+ via the reaction As an example estimation of f , assume that XH is deuter- 2 ated to form XHD+ on one-half of the reactions with ID+,and + + H2D + CO −→ DCO + H2 (6) the deuterated ion then dissociatively recombines with electrons + while the normal isotopologue HCO+ is produced mainly via the to form XD H on one-half of the reactions. The neutral XD + + is then destroyed by a number of ions in the model including corresponding reaction with H . A similar story holds for N2D + 3 non-protonating ions such that the effective rate of destruction and N H . As an example of the latter, consider the species 2 is 2 times the rate of reaction with protonating ions IH+. Solving NH2D. After NH3 is formed, it undergoes destruction by ions, + for the abundance ratio of XD to XH then yields f = 1/8. As one of which is the reaction with H2D to lead to the deuterated + the temperature rises, the second term lessens but deuteration ion NH3D . This ion can then undergo dissociative recombina- + ff can still occur during the formation of a species via processes tiontoformNH2D H among other products. A di erent mech- + + ffi anism can occur for radicals such as OH, in which rapid reaction that lead back to CH2D and C2HD or, less e ciently, through destruction of XH via these ions or secondary non-deuterating with atomic deuterium leads to the deuterated isotopologue. At steady-state, one can show that the XD/XH abundance ones initiating processes that eventually produce XD. ratio between relatively non-reactive species (non-radicals) is Let us now see whether we can analyze the temperature and density dependence of selected abundance ratios of deuterated approximately the following: to normal isotopologues of secondary species using the simple + +/ + XD ≈ PXD + ID analysis embodied in Eq. (7). For the ionic ratios DCO HCO f + (7) +/ + XH PXH IH and N2D N2H , deuteration occurs during the production of these species. Figure 2 shows that the temperature dependence where the two terms on the right refer to deuteration via for- + + is essentially monotonic, following that of H D /H since these mation and destruction routes respectively. Here P stands for the 2 3 ions are their major precursors. In addition, there is little density production rate, which can come from any of the three parent ion + + + + dependence except for DCO /HCO , which increases for warm- pairs, and ID and IH stand for the total abundance of deuter- 6 −3 + + + + core abundances at densities higher than 10 cm at the larger ating ions (H D ,DCO ...) and protonating ions (H ,HCO ...) 2 3 temperatures. This effect may derive from a secondary formation respectively. What is omitted from this equation are destruction + + route involving CH (CH D )andO: pathways of XH leading to XD via routes more complex than 3 2 simple deuteration. The factor f in the equation is the efficiency + + CH + O −→ HCO + H2, (9) ( f ≤ 1) with which the ID+/IH+ abundance ratio is transfered to 3 + + the secondary pair. It can be estimated from more detailed results CH2D + O −→ DCO + H2, (10) by working out the steady-state kinetics of the formation of XD from XH and its destruction via all ions. The derivation leads to since this primary abundance ratio does show a similar density the formula dependence. The species we will now consider – HCN, HNC, H2CO, f = f1/ f2, (8) and NH3 – are all neutral ones and can in principal be deuterated where f1 is the fraction of deuterations of XH that lead to XD during formation and destruction. Yet, except for ammonia and + and f2 is the ratio of the abundance of IH to the total abundance HNC, the direct destructive route is blocked for an assortment E. Roueff et al.: Deuterium fractionation in warm clumps 249

+ One route comes directly from CH2D : + + CH2D + N −→ DNC + H2, (11)

+ + CH2D + N −→ DCN + H2, (12)

where the two channels are assumed to have equal rate coeﬃ- cients. It should be noted that the lower energy isomer of the ionized form of HCN is HNC+ and not HCN+ (Hansel et al. 1998). The separate forms DNC+ and DCN+ show diﬀerent be- havior in the chemical chain of reactions: + + + DNC + H2 −→ DNCH + H, DHNC + H, (13)

+ + DCN + H2 −→ DCNH + H. (14)

The subsequent dissociative recombination reactions proceed as: DCNH+ + e− −→ DCN + H, (15)

DNCH+ + e− −→ DNC + H, (16)

DHNC+ + e− −→ DNC + H. (17) Fig. 3. Deuterium fractionation ratios. Left: warm-core conditions, The other channels right: low-metal conditions. DCNH+ + e− −→ HNC + D, (18)

DNCH+ + e− −→ HCN + D, (19) of reasons. First, consider H2CO. As shown by Osamura et al. + + − (2005), deuteration of formaldehyde leads to the ion H2COD , DHNC + e −→ HNC + D, (20) with the deuterium on the opposite side of the molecule from the hydrogens. Dissociative recombination then leads just to are assumed to take place with an efficiency smaller by a factor H2CO + D rather than to HDCO + H, so that no deuteration of 2 than the channel leading to deuteration (Roueff 2005), fol- is accomplished unless there is significant internal rearrange- lowing some experimental results on deuterated molecular ions. ment during recombination, which is assumed not to be the case We have not yet explained the strong density dependence here. For HCN and HNC, the story is a little more complex. / + of the DCN HCN abundance ratio, which exceeds that of the Two protonated ionic forms exist: HCNH , which is linear, and primary ion ratio CH D+/CH+, especially for the low-metal el- + 2 3 H2NC , which is Y-shaped (Talbi & Herbst 1998). Protonation emental abundances. Two main factors contribute to this en- + of HCN leads to the linear ion HCNH while protonation of hancement. As density increases, not only the abundance of the + + + + HNC leads both to this ion and to the Y-shaped structure H2NC . CH ion is enhanced but also those of CH D and CH D be- + 5 4 3 2 Deuteration of HCN leads to the linear ion DNCH , which, upon cause these species are produced via radiative association of the dissociative recombination with electrons, can produce HCN + +/ + primary ions with H2,HDandD2.TheCH4D CH5 ratio is al- D, DNC + H, and CN + H + D, but not DCN. On the other ways larger than the CH D+/CH+ with the present chemistry. + 2 3 hand, deuteration of HNC leads to the ion DCNH and the non- Dissociative recombination of CH D+ and CH D+ leads to rad- + + 4 3 2 linear ion DHNC . Dissociative recombination of DCNH can icals such as CHD and CD2 that react with atomic nitrogen to then lead to DCN + H, whereas dissociative recombination of produce DCN. In addition, the main destruction routes of DCN + + + + DHNC can lead to DNC H. Thus deuteration of HCN leads to are the reactions with the abundant ions HCO and H3O that DNC only whereas deuteration of HNC leads to both DCN and give DCNH+, which subsequently returns to DCN via dissocia- DNC. At low temperatures, where the HNC/HCN abundance ra- tive recombination. A further destruction route is the reaction of tio is near unity, deuteration of HCN through HNC is important. DCN + H leading to HCN + D, the importance of which de- We assume, however, that the reaction of HNC with atomic oxy- creases with density. Unlike DCN/HCN, the DNC/HNC abun- gen yields CO in an exothermic channel with a small barrier dance ratio is thought to be not relevant at high tempera- (Pineau des Forêts et al. 1990; Schilke et al. 1992). Then, as the tures, since destruction of both species via reaction with atomic temperature rises, the abundance of HNC decreases due to the oxygen means that neither can be detected. For completeness, neutral-neutral reaction with atomic oxygen, and so deuteration however, the ratio is shown in the bottom panels of Fig. 3. of HCN through HNC becomes unimportant. Let us now consider the often observed abundance ratios in- The abundance ratio DCN/HCN is shown in the top panels volving singly and doubly deuterated isotopologues of formalde- of Fig. 3 for warm-core and low-metal elemental abundances, hyde, both of which are shown in Fig. 4. The former case is +/ + respectively. At low temperatures, the deuteration proceeds strongly related to the CH2D CH3 ratio since these ions eventu- through HNC as discussed above. The dependence on temper- ally lead to their neutral counterparts, which react with O atoms ature decreases monotonically from 20 K upwards. By 50 K, to form formaldehyde and its isotopologue. And, the temper- however, the ratio is still equal to or greater than 0.01 at the high- ature profiles are generally in accord with this simple picture. + + est densities considered, which far exceeds the H2D /H value As with the DCN/HCN ratio, however, the density dependence +/ + 3 / and so derives mainly from CH2D CH3 . What exactly are the of HDCO H2CO is stronger than one might expect based on formation routes of DCN and DNC at these higher temperatures? our simple picture, and may also involve a significant role for 250 E. Roueff et al.: Deuterium fractionation in warm clumps

Fig. 4. Deuterium fractionation ratios. Left: warm-core conditions, Fig. 6. Deuterium fractionation ratios. Left: warm-core conditions, right: low-metal conditions. right: low-metal conditions.

formation of ammonia and its deuterated isotpologue is a complex affair, it is not facile to find the specific cause of the en- hancement in the NH2D/NH3 abundance ratio. According to Turner (2001), NH2D at low temperatures is formed primarily + from the radical NH2 via deuteration to form NH2D , which then + reacts with H2 to form NH3D + H. Dissociative recombination of this ion then leads to NH2D. We found some indication that, + even at 50 K, NH2D is an important precursor to NH2D. Finally, we consider the case of the abundance ratio / +/ + C2D C2H, which is closely related to C2HD C2H2 . Figure 6 contains plots of both ratios for warm-core and low-metal elemental abundances. Although the temperature dependence of C2D/C2H presents no surprises, the density dependence with warm-core elemental abundances is an example of a maximum ≈ at intermediate densities. It is clear that at densities above nH2 3 × 105 cm−3, the ratio begins to decrease. At these same densities, the abundance ratio of the primary ion precursors still increases but by a small amount. The explanation is as follows: as the density increases the fractional abundances of the + C2H2 ion and its deuterated isotopologue are gradually reduced Fig. 5. Deuterium fractionation ratios. Left: warm-core conditions, compared with the fractional abundances of the secondary ion + right: low-metal conditions. C2H and its deuterated isotopologue. Since the abundance ratio 3 +/ + +/ + C2H2D C2H3 is less than the abundance ratio C2HD C2H2 , the production of C2DandC2H via the more saturated ions +/ + leads to a lower abundance ratio. The case of the low-metal ele- CH4D CH5 . Doubly deuterated formaldehyde presumably derives from CHD+ and CH D+. mental abundances is different because the increase in the ratio 2 3 2 +/ + We display in Fig. 5 both NH2D/NH3 and HDO/H2O, since C2HD C2H2 with increasing density is much less (note the dif- water and ammonia can be abundant in interstellar clouds. Much ference in the y-scales of the panels for the two sets of elemental / of the deuteration occurs during the destruction phase for these abundances), so that the decrease in the C2D C2H ratio sets in two species, and the abundance ratio HDO/H2O generally fol- earlier. +/ + lows that of H2D H3 especially for low-metal abundances. Still, Table 2 shows the predicted ratios for species discussed there appears to be another mechanism allowing the abundance above at molecular hydrogen densities of 105,106, and 107 cm−3 / +/ + ratio NH2D NH3 to exceed H2D H3 , often by a considerable and at temperatures of 50, 60, and 70 K for both warm-core amount. A detailed analysis of the formation and destruction re- (WC) and low-metal (LM) elemental abundances, while Table 3 + actions shows that NH3D , the precursor to NH2D, is not formed shows the calculated fractional abundances of the normal iso- primarily from the deuteration of NH3 so that the dominant pro- topologues with respect to molecular hydrogen under the same cess leading to NH2D occurs during its formation. Since the conditions. Other values are available from the authors. E. Roueff et al.: Deuterium fractionation in warm clumps 251

Table 2. Calculated abundance ratios between selected singly deuter- Table 3. Calculated fractional abundances relative to molecular hydro- ated and normal isotopologues. gen for normal isotopologues.

Species n(H2)XD/XH abundance ratio Species n(H2) Fractional abundance 50 K 60 K 70 K 50 K 60 K 70 K cm−3 WC LM WC LM WC LM cm−3 WC LM WC LM WC LM + 5 + 5 H3 10 2.5(–3) 3.0(–3) 1.3(–3) 1.5(–3) 8.1(–4) 8.6(–4) H3 10 4.5(–10) 1.3(–09) 4.4(–10) 1.4(–09) 4.4(–10) 1.3(–09) 106 2.5(–3) 3.0(–3) 1.3(–3) 1.5(–3) 8.1(–4) 8.6(–4) 106 4.7(–11) 1.4(–10) 4.7(–11) 1.4(–10) 4.6(–11) 1.4(–10) 107 2.5(–3) 3.0(–3) 1.3(–3) 1.5(–3) 8.1(–4) 8.6(–4) 107 5.0(–12) 1.4(–11) 4.9(–12) 1.4(–11) 4.9(–12) 1.4(–11) + 5 + 5 CH3 10 2.7(–2) 4.4(–2) 1.3(–2) 1.5(–2) 6.1(–3) 6.6(–3) CH3 10 1.7(–11) 2.8(–11) 2.3(–11) 3.2(–11) 2.9(–11) 3.3(–11) 106 3.7(–2) 4.6(–2) 1.4(–2) 1.6(–2) 6.4(–3) 6.6(–3) 106 5.9(–13) 5.9(–14) 8.4(–13) 1.5(–12) 7.6(–13) 1.6(–12) 107 4.0(–2) 4.6(–2) 1.5(–2) 1.6(–2) 6.5(–3) 6.6(–3) 107 1.4(–14) 5.7(–14) 1.6(–14) 6.4(–14) 1.7(–14) 7.0(–14) + 5 + 5 C2H2 10 7.5(–2) 0.21 6.0(–2) 0.14 3.9(–2) 6.3(–2) C2H2 10 5.6(–13) 7.3(–13) 9.8(–13) 7.4(–13) 1.5(–12) 7.5(–13) 106 0.16 0.23 0.11 0.15 5.7(–2) 6.5(–2) 106 2.9 (–15) 3.2(–14) 5.0(–15) 3.5(–14) 4.1(–15) 3.7(–14) 107 0.19 0.24 0.13 0.15 6.2(–2) 6.6(–2) 107 4.3(–17) 1.4(–15) 4.6(–17) 1.6(–15) 4.7(–17) 1.8 (–15) HCO+ 105 8.9(–4) 1.2(–3) 4.8(–4) 5.6(–4) 2.9(–4) 3.2(–4) HCO+ 105 1.4(–09) 1.5(–08) 1.4(–09) 1.7(–08) 1.4(–09) 1.7(–08) 106 8.6(–4) 1.1(–3) 4.5(–4) 5.1(–4) 2.7(–4) 3.0(–4) 106 6.6(–10) 5.0(–09) 6.6(–10) 5.3(–09) 6.6(–10) 5.5(–09) 107 1.2(–3) 1.0(–3) 6.7(–4) 4.9(–4) 4.1(–4) 2.9(–4) 107 1.7(–10) 1.6(–09) 1.7(–10) 1.6(–09) 1.7(–10) 1.7(–09) + 5 + 5 N2H 10 8.0(–4) 9.8(–4) 4.2(–4) 4.7(–4) 2.6(–4) 2.8(–4) N2H 10 7.1(–11) 2.7(–10) 7.5(–11) 2.9(–10) 7.8(–11) 2.9(–10) 106 8.0(–4) 9.6(–4) 4.2(–4) 4.7(–4) 2.6(–4) 2.7(–4) 106 9.2(–12) 3.0(–11) 9.8(–12) 3.1(–11) 1.0(–11) 3.2(–11) 107 8.2(–4) 9.6(–4) 4.3(–4) 4.7(–4) 2.6(–4) 2.7(–4) 107 8.7(–13) 3.1(–12) 9.6(–13) 3.1(–12) 1.2(–12) 3.2(–12) HCN 105 3.1(–3) 9.1(–3) 1.2(–3) 2.8(–3) 5.1(–4) 1.1(–3) HCN 105 4.6(–08) 3.2(–09) 5.7(–08) 2.6(–09) 6.7(–08) 2.1(–09) 106 6.3(–3) 1.7(–2) 2.1(–3) 4.7(–3) 8.2(–4) 1.9(–3) 106 2.4(–09) 4.3(–10) 2.9(–09) 3.4(–10) 2.3(–09) 2.7(–10) 107 9.4(–3) 2.5(–2) 3.0(–3) 6.6(–3) 1.0(–3) 2.7(–3) 107 2.1(–10) 6.1(–11) 1.9(–10) 4.7(–11) 1.7(–10) 3.8(–11) HNC 105 2.7(–3) 3.3(–3) 1.2(–3) 1.2(–3) 5.8(–4) 5.9(–4) HNC 105 1.0(–10) 7.5(–11) 9.5(–11) 5.3(–11) 8.8(–11) 3.8(–11) 106 5.4(–3) 3.2(–3) 2.4(–3) 1.2(–3) 1.1(–3) 6.0(–4) 106 1.3(–12) 2.9(–12) 1.2(–12) 1.9(–12) 8.1(–13) 1.4(–12) 107 5.4(–3) 3.1(–3) 2.2(–3) 1.2(–3) 9.4(–4) 6.1(–4) 107 5.4(–14) 1.1(–13) 4.0(–14) 7.3(–14) 3.2(–14) 5.3(–14) 5 5 H2O103.1(–4) 5.9(–4) 1.6(–4) 2.6(–4) 9.9(–5) 1.5(–4) H2O101.2(–06) 6.5(–07) 1.3(–06) 6.4(–07) 1.4(–06) 6.3(–07) 106 3.7(–4) 5.2(–4) 1.9(–4) 2.4(–4) 1.2(–4) 1.4(–4) 106 8.6(–07) 2.7(–07) 9.0(–07) 2.6(–07) 9.3(–07) 2.5(–07) 107 5.6(–4) 4.9(–4) 3.0(–4) 2.3(–4) 1.9(–4) 1.4(–4) 107 7.2(–07) 1.0(–07) 7.5(–07) 9.8(–08) 7.5(–07) 9.6(–08) 5 5 H2CO 10 1.7(–2) 2.1(–2) 8.3(–3) 8.6(–3) 3.9(–3) 3.6(–3) H2CO 10 3.7(–10) 4.2(–09) 4.1(–10) 4.1(–09) 4.4(–10) 3.6(–09) 106 2.5(–2) 2.2(–2) 1.2(–2) 1.2(–2) 4.8(–3) 4.7(–3) 106 2.2(–11) 2.9(–10) 2.6(–11) 3.1(–10) 2.0(–11) 2.9(–10) 107 4.3(–2) 2.6(–2) 2.6(–2) 1.8(–2) 8.7(–3) 7.0(–3) 107 1.3(–12) 2.0(–11) 1.3(–12) 2.6(–11) 1.2(–12) 2.4(–11) 5 5 NH3 10 2.2(–3) 1.4(–3) 1.6(–3) 6.5(–4) 1.3(–3) 3.5(–4) NH3 10 2.5(–08) 1.1(–07) 2.5(–08) 1.2(–07) 2.4(–08) 1.2(–07) 106 2.2(–3) 1.2(–3) 1.5(–3) 5.9(–4) 1.2(–3) 3.5(–4) 106 2.6(–08) 4.5(–08) 2.5(–08) 4.5(–08) 2.5(–08) 4.5(–08) 107 3.6(–3) 1.2(–3) 1.6(–3) 5.7(–4) 9.5(–4) 3.4(–4) 107 2.1(–08) 1.6(–08) 2.3(–08) 1.6(–08) 2.6(–08) 1.6(–08) 5 5 C2H103.9(–2) 3.9(–2) 3.2(–2) 2.1(–2) 2.1(–2) 9.8(–3) C2H106.9(–10) 1.7(–09) 5.2(–10) 7.9(–10) 4.4(–10) 4.2(–10) 106 3.6(–2) 3.0 (–2) 2.7(–2) 1.4 (–2) 1.4(–2) 6.7(–3) 106 3.5(–12) 9.9(–11) 1.8(–12) 4.1(–11) 7.5(–13) 2.1(–11) 107 2.5(–2) 2.5(–2) 1.2(–2) 1.0(–2) 5.9 (–3) 5.1(–3) 107 7.6(–14) 4.6(–12) 2.9(–14) 1.9(–12) 1.4(–14) 9.7(–13)

4. Discussion densities that exceed 106 cm−3, whereas for the low-metal case, In order to understand the result of Leurini et al. (2006) that the a similar result is obtained at the higher temperature of 60 K. DCN/HCN abundance ratio is nearly 0.01 in warm (50−75 K) Although we do not expect a steady-state calculation to be as ac- 7 −3 dense (nH = 1−4 × 10 cm ) clumps in the Orion Bar, we have curate for fractional abundances of organic species, we do obtain used a gas-phase steady-state model to calculate the extent of a fractional abundance for HCN of 2−3×10−9 at a molecular hy- deuterium fractionation at temperatures up to 70 K over a wide drogen density of 106 cm−3 in the warm-core conditions, almost range of densities. The calculations are based on two different independently of the temperature range between 50 and 70 K. sets of elemental abundances: one labeled “warm-core” abun- This value is surprisingly close to the observed derived frac- dances, in which higher values of heavy elements are used to tional density in the Orion Bar by Leurini et al. (2006) of ≈1.5 × account for partial evaporation of grain mantles, and the other, 10−9, assuming LTE, an H13CN/HCN ratio of 1/70 and a total 22 −2 the more standard “low-metal” abundances. We have attempted column density for H2 of 9 × 10 cm . At lower densities and to interpret the results of the calculations in terms of primary higher temperatures, which pertain to the inter-clump medium abundance ratios between ions that undergo deuterium exchange (150 K, 5 × 105 cm−3), we would expect to see little deutera- reactions although the effects on secondary species are often tion, mainly because of the high kinetic temperature. The inter- overlapping. Nevertheless, at the higher temperatures studied, clump material is perhaps best mapped out by formaldehyde. If the higher abundance ratios obtained between singly deuterated a limited amount of formaldehyde is to be found in the warm + and normal isotopologues tend to derive from the ions CH2D clumps, and our model results show this to be the case at a level + + + −9− −11 and CH3 (and to a lesser extent from C2HD and C2H2 ), as of about 10 10 depending on the depletions and physical realized by Leurini et al. (2006) since the primary ionic ratio conditions, then HDCO might also be profitably searched for in +/ + H2D H3 is too small. these regions, since our calculations also show that deuterium With both sets of elemental abundances, we obtain that the fractionation is high for formaldehyde at temperatures through DCN/HCN ratio is a strong direct function of density. For the 70 K. Indeed, at 60 K, we obtain that HDCO/H2CO is close warm-core case, we calculate that at a temperature of 50 K, we to ≈0.01 even at the lowest densities for both sets of elemental can explain the measured DCN/HCN value of 7−9 × 10−3 at gas abundances. 252 E. Roueff et al.: Deuterium fractionation in warm clumps

It would be desirable to both expand the limited frequency Gerlich, D., Herbst, E., & Roueff, E. 2002, Planet. Space Sci., 50, 1275 range studied by the APEX survey to search more completely Grevesse, N., Noels, A., & Sauval, A. J. 1996, in ASP Conf. Ser., ed. S. S. Holt, for other molecules and their deuterated isotopologues and to re- & G. Sonneborn (San Francisco: ASP), 90, 117 Hansel, A., Glantschnig, M., Scheiring, C., Lindinger, W., & Ferguson, E. E. port some upper limits for species not detected. As an example, 1998, J. Chem. Phys., 109, 1743 we find a high fractional abundance of ammonia, so that even Herbst, E., Adams, N. G., Smith, D., & Defrees, D. J. 1987, ApJ, 312, 351 with our calculated lower abundance ratios of ≈10−3 between Le Bourlot, J., Pineau des Forêts, G., Roueff, E., & Flower, D. R. 1995, A&A, the deuterated and normal isotopologues, it might still be possi- 302, 870 Leurini, S., Rolffs, R., Thorwirth, S., et al. 2006, A&A, 454, L47 ble to detect NH2D, which has two relatively low-lying transi- Lis, D. C., & Schilke, P. 2003, ApJ, 597, L145 tions at 282 GHz and 305.7 GHz (respectively para and ortho). Millar, T. J. 2002, Planet. Space Sci., 50, 1189 Likewise, it would be interesting to see if HNC, which possesses Millar, T. J., Bennett, A., & Herbst, E. 1989, ApJ, 340, 906 no transitions within the observed frequency range, cannot be Moustefaoui, T., Rebrion-Rowe, C., Le Garrec, J.-L., Rower, B. R., & Mitchell, detected from these warm clumps, since our prediction that it J. B. A. 1998, Faraday Discussions, 109, 71 Nagaoka, A., Watanabe, N., & Kouchi, A. 2005, ApJ, 624, L29 has a low fractional abundance is based on the destruction re- Osamura, Y., Roberts, H., & Herbst, E. 2004, A&A, 421, 1101 action with atomic oxygen, which has not been studied in the Osamura, Y., Roberts, H., & Herbst, E. 2005, ApJ, 621, 348 laboratory, to the best of our knowledge. Finally, we predict a Parise, B., Castets, A., Herbst, E., et al. 2004, A&A, 416, 159 5 −3 Parise, B., Ceccarelli, C., Tielens, A. G. G. M., et al. 2002, A&A, 393, L49 sufficiently high abundance of C2D at a density of ≈10 cm Parise, B., Ceccarelli, C., Tielens, A. G. G. M., et al. 2006, A&A, 453, 949 that it may well be detectable. Pineau des Forêts, G., Roueff, E., & Flower, D. R. 1990, MNRAS, 244, 668 Roberts, H., & Millar, T. J. 2000, A&A, 364, 780 Roberts, H., Herbst, E., & Millar, T. J. 2002, MNRAS, 336, 283 Acknowledgements. E.H. thanks the National Science Foundation for its support Roberts, H., Herbst, E., & Millar, T. J. 2003, ApJ, 591, L41 of his research program in astrochemistry and thanks the Observatoire de Paris Roberts, H., Herbst, E., & Millar, T. J. 2004, A&A, 424, 905 for providing funds to enable him to travel to Meudon, where much of the work Roueff, E. 2005, J. Phys. Conf. Ser., 4, 1 was accomplished. B.P. is grateful to the Alexander von Humboldt Foundation Roueff, E., Lis, D. C., van der Tak, F. F. S., Gerin, M., & Goldsmith, P. F. 2005, for a research fellowship. The authors thank the referee, Paola Caselli, for her A&A, 438, 585 thoughtful comments. Schilke, P., Walmsley, C. M., Pineau Des Forêts, G., et al. 1992, A&A, 256, 595 Smith, D., Adams, N. G., & Alge, E. 1982, ApJ, 263, 123 Stantcheva, T., & Herbst, E. 2003, MNRAS, 340, 983 References Talbi, D., & Herbst, E. 1998, A&A, 333, 1007 Tielens, A. G. G. M. 1983, A&A, 119, 177 Aikawa, Y., Herbst, E., Roberts, H., & Caselli, P. 2005, ApJ, 620, 330 Turner, B. E. 2001, ApJS, 136, 579 Asvany, O., Schlemmer, S., & Gerlich, D. 2004, ApJ, 617, 685 Vastel, C., Phillips, T. G., & Yoshida, H. 2004, ApJ, 606, L127 Charnley, S. B., Tielens, A. G. G. M., & Rodgers, S. D. 1997, ApJ, 482, L203 Wakelam, V., Herbst, E., & Selsis, F. 2006, A&A, 451, 551 Gerin, M., Lis, D. C., Philipp, S., et al. 2006, A&A, 454, L63 Walmsley, C. M., Flower, D. R., & Pineau des Forêts, G. 2004, A&A, 418, 1035 Gerlich, D., & Schlemmer, S. 2002, Planet. Space Sci., 50, 1287